To dry in a dehydrator, begin by placing the halved tomatoes cut-side up on the racks. Stack the racks and leave to dry for 2-3 hours. The tomatoes will feel dry and will darken in color. They should not be brittle or crisp.

To oven-dry the tomatoes, begin by lining a large cookie sheet with aluminum foil, and place a rack on top of the foil. Place the halved tomatoes cut-side up on the rack, making sure that they do not touch. Place the cookie sheet in a 200 degree oven and leave to dry for 4-5 hours. They should feel dry and will darken in color.

Sterilize four 8 oz. jars with their lids by boiling them in a large pot of water for 10 minutes. Using tongs, remove the jars and lids from the water, and allow to cool on a dry surface. Place 1 clove of garlic in the bottom of each jar. Begin layering the dried tomatoes. When half full, tuck in 3-4 basil leaves and 1 sprig of rosemary, and then continue layering dried tomatoes until almost reaching the top. Pack down slightly with a spoon. Pour olive oil over the top and make sure they are thoroughly immersed in the oil. Wipe clean the rims of the jars and seal with their lids. Label and date the jars. Store in the refrigerator for up to several months. The oil in the jars can be pureed with the dried tomatoes for making a pesto, or to flavor bread, pastas, or vegetables.